Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?
Solution
For a, b, c<br><br>mean = $\overline x = {{a + b + c} \over 3}$<br><br>$\overline x = {{2b} \over 3}$<br><br>We know, S.D. of a + 2, b + 2, c + 2 = S.D. of a, b, c = d<br><br>${d^2} = {{{a^2} + {b^2} + {c^2}} \over 3} - {{4{b^2}} \over 9}$<br><br>${b^2} = 3{a^2} + 3{c^2} - 9{d^2}$
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Dispersion
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